The classification problem is an important topic in knowledge discovery and machine learning. Traditional classification tree methods and their improvements have been discussed widely. This work proposes a new approach to construct decision trees based on discriminant functions which are learned using genetic programming. A discriminant function is a mathematical function for classifying data i...

A new technique is described for explicitly evaluating quotients of the Dedekind eta function at quadratic integers. These evaluations do not make use of complex approximations but are found by an entirely ‘algebraic’ method. They are obtained by means of specialising certain modular equations related to Weber’s modular equations of ‘irrational type’. The technique works for a large class of et...

Starting from the analytic class number formula involving its Lfunction, we first give an expression for the class number of an imaginary quadratic field which, in the case of large discriminants, provides us with a much more powerful numerical technique than that of counting the number of reduced definite positive binary quadratic forms, as has been used by Buell in order to compute his class ...

This study investigated the relationship of self-efficacy for verbal fluency, academic self-efficacy, and depression between adolescents who stutter and fluent speakers. Two separate discriminant function analyses were performed. The first analysis used the self-efficacy and depression scores as response variables and fluency classification as the grouping variable. Results indicated that self-...

The famous results of Gross and Zagier compare the heights of Heegner points on modular curves with special values of the derivatives of related L-functions. When specialized to the level 1 case (i.e., the full modular curve H/Γ, where Γ = SL2(Z)), we recover an astounding formula for the differences of singular moduli (the Heegner points on the full modular curve) in terms of an explicit prime...

Over the past decades, there has been an increase of attention to adapting machine learning methods fully exploit higher order structure tensorial data. One problem great interest is tensor classification, and in particular extension linear discriminant analysis multilinear setting. We propose a novel method for that radically different from ones considered so far, it first tensors quadratic an...

Let $A$ be a non-isotrivial ordinary abelian surface over global function field of characteristic $p>0$ with good reduction everywhere. Suppose that does not have real multiplication by any quadratic discriminant multiple $p$ . We prove there are infinitely many places modulo which is isogenous to the product two elliptic curves.

Two groups of pattern-recognition algorithms for hybrid optical-digital computer processing are theoretically and experimentally compared. The first group is based on linear mapping, while the second group is based on feature extraction and eigenvector analysis. We study the relations among various linear-mapping-based algorithms by formulating a more general unified pseudoinverse algorithm. We...